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Shallow Footing Failure

The modes of failure caused by a footing of width B subject to a uniform pressure q develop the limiting soil shear strength ts at a given point along a slip path is dipected in the figure above. The force on a unit width of footing causing shear is q times B. The force resisting shear is ts times the length of the slip path ’abc’. The force resisting shear in a purely cohesive soil is c ’abc’ and in a purely friction soil σn tan Φ ’abc’. The length of the slip path ’abc’ resisting failure increases in proportion to the width of footing B. The figure shows a right side rotation shear failure along a well defined and continuous slip path ’abc’ which will result in bulging of the soil adjacent to the foundation. The wedge under the footing goes down and the soil is pushed to the side laterally and up. Surcharge above and outside the footing helps hold the block of soil down. Most bearing capacity failures occur in general shear under stress controlled conditions and lead to tilting and sudden catastrophic movements. Dense sands and saturated clays loaded rapidly are practically incompressible and may fail in general shear. After failure, a small increase in stress causes large additional settlement of the footing. The bulging of surface soil may be evident on the side of the foundation undergoing a shear failure. In relatively rare cases, some radial tension cracks may be present. Shear failure has been found to occur more frequently under shallow foundations supporting silos, tanks, and towers than under conventional buildings. Shear failure usually occurs on only one side because soils are not homogeneous and the load is often not concentric. Depth of Failure. Depth of shear zone H may be approximated by assuming that the maximum depth of shear failure occurs beneath the edge of the foundation. using Θ =45 + Φ’/2 , then H = BTan( Θ) H = BTan(45+ Θ'/2) where H = depth of shear failure beneath foundation base, ft B = footing width, ft Θ =45 + Φ’/2, deg Φ’ = effective angle of internal friction, deg The depth H for a shear failure will be 1.73B if Φ’ = 30°, a reasonable assumption for soils. H therefore should not usually be greater than 2B. If rigid material lies within 2B, then H will be < 2B and will not extend deeper than the depth of rigid material. Horizontal Length of Failure. The length that the failure zone extends from the foundation perimeter at the foundation depth L may be approximated by L = (H+D)Tan(Θ) L = (H+D)Tan(45+ Φ'/2) where D is the depth of the foundation base beneath the ground surface. L ~ 1.73(H + D) if Φ’ = 30 deg. The shear zone may extend horizontally about 3B from the foundation base.

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